Voltage difference across a resistance in a circuit can be calculated by using equation (5):

v = 12sin (4πt)

Where v is the voltage difference across the resistance in Volt and t is the time in second. The voltage root mean square (RMS) value over a range of a ≤ t ≤ b can be calculated by using the formula (1).

vᵣₘₛ = √(1/(b - a) ∫ₐᵇ v²)dt) Formula (1)

You are asked to find the RMS value of voltage over a range of 0 ≤ t ≤ 0.8s by using:

a) Using an analytical integration